In the framework of mutually unbiased bases (MUBs), a measurement in one basis gives no information about the outcomes of measurements in another basis. Here we relax the no-information condition by allowing the $d$ outcomes to be predicted according to a predefined probability distribution $q=(q_0,...,q_{d-1})$. The notion of mutual unbiasedness, however, is preserved by requiring that the extracted information is the same for any preparation and any measurement; regardless of which state from which basis is chosen to prepare the system, the outcomes of measuring the system with respect to the other basis generate the same probability distribution. In light of this, we define the notion of mutually equibiased bases (MEBs) such that within each basis the states are equibiased with respect to the states of the other basis and that the bases are mutually equibiased with respect to each other. For $d=2,3$, we derive a set of $d+1$ MEBs. The mutual equibiasedness imposes nontrivial constraints on the distribution $q$, leading, for $d=3$, to the restriction $1/3\le \mu \le 1/2$, where $\mu ={\sum }_{k=0}^2{q}_k^2$. To capture the incompatibility of the measurements in MEBs, we derive an inequality for the probabilities of projective measurements in a qudit system, which yields an associated entropic uncertainty inequality. Finally, we construct a class of positive maps and their associated entanglement witnesses based on MEBs. While an entanglement witness constructed from MUBs is generally finer than one based on MEBs when both use the same number of bases, for certain values of the index $\mu$, employing a larger set of MEBs can yield a finer witness. We illustrate this behavior using isotropic states of a $3\times 3$ system. Our results reveal that not all bases in a set of $L$ MEBs can contribute to the entanglement detection. A constraint, dependent on the probability distribution $q$, limits the number of MEBs that can be employed.

We prove that the parity protocol is optimal for a general class of nonadaptive distillation protocols of all $n$-player nonlocal boxes (NLBs) based on xor games. The conditional distributions generated by these NLBs are assumed to have trivial local marginals. We also show that already for $n=2$, parity is no longer optimal if the local marginals are nontrivial. The or protocol is shown to perform better and in the process also slightly extend the known correlations that collapse communication complexity. This emphasizes again the need to understand the local properties of nonlocal systems in order to obtain a better characterization of the global behavior. We conclude by showing an equivalence between adaptive distillation protocols that use identical NLBs and parity protocol using nonidentical NLBs.

In this work we explore how different types of resources are distributed among the states generated by quantum random circuits. We focus on multipartite nonlocality, but we also analyze quantum correlations by appealing to different entanglement and nonclassicality measures. We analyze the violation of Mermin and Svetlichny inequalities in order to get a glance at the distribution of nonlocality and genuine multipartite nonlocality. Next, we compare universal vs nonuniversal sets of gates, to gain insight into the problem of explaining quantum advantage. By comparing the results obtained with ideal (noiseless) vs noisy intermediate-scale quantum devices, we lay the basis of a certification protocol, which aims to quantify how robust is the resources distribution among the states that a given device can generate. We have implemented our nonlocality-based benchmark on actual quantum processors with different architectures, in order to assess up to which point they are capable of reproducing the ideal results.

Genuine multipartite entanglement (GME) represents the strongest form of entanglement in multipartite systems, providing significant advantages in various quantum information processing tasks. In this work, we propose an experimentally feasible scheme for detecting GME, based on the truncated moments of positive maps. Our method avoids the need for full state tomography, making it scalable for larger systems. We provide illustrative examples of both pure and mixed states to demonstrate the efficacy of our formalism in detecting inequivalent classes of tripartite genuine entanglement. We further demonstrate the detection of quadripartite genuine entanglement, underscoring the effectiveness of our method in identifying entanglement beyond the tripartite case. Finally, we present a proposal for realizing these moments in real experiments.

Controlled quantum gate teleportation (CQGT) enables controller-regulated quantum gate transmission in distributed networks. The current CQGT scheme faces security challenges as both genuine tripartite entanglement and insecure classical-quantum hybrid resources can achieve high standard metrics (fidelity or control power). In this paper, we propose a device-independent (DI) CQGT verification scheme using genuine tripartite nonlocality in black-box scenarios. In the quantum cnot gate teleportation, our DI verification scheme based on Svetlichny inequality achieved the maximum inequality violation, which is superior to the traditional Clauser-Horne-Shimony-Holt (CHSH) type scheme. It is crucial that we establish a direct relationship between Svetlichny inequality violation and the effective control power (ECP) of the controller in eavesdropping depolarization channels, where ECP corresponds to the maximum inequality violation. This work addresses critical security verification gaps in CQGT protocols while highlighting the fundamental role of multipartite nonlocality in quantum information processing.

The leading-order two-loop vacuum-polarization potential, linear in the Coulomb field of a nucleus, was first derived in the seminal 1955 work of Källén and Sabry [Dan. Mat. Fys. Medd. 29, 1 (1955)]. The higher-order two-loop vacuum-polarization corrections, however, have remained unknown until now. In this work, we compute Coulomb corrections to the Källén-Sabry potential, specifically those involving three, five, and seven Coulomb interactions inside the vacuum-polarization loop. The potentials are evaluated in momentum space and subsequently used to calculate one-electron energy shifts. Our results reduce the theoretical uncertainty of the two-loop vacuum-polarization contribution to transition energies, which is required for next-generation tests of bound-state QED in heavy one- and few-electron ions as well as for the determination of nuclear charge radii.

High-accuracy extreme ultraviolet (EUV) spectroscopy of the $1s^{2}2s2p {}^{1}P_1\text{−}1s^{2}2s^2 {}^{1}S_0$ electric dipole ($E1$) transitions in beryllium-like ${\mathrm{S}}^{12+}$ and $\mathrm{C}{\mathrm{l}}^{13+}$ was performed at the Shanghai High-Temperature Superconducting Electron Beam Ion Trap. Utilizing a portable high-resolution soft x-ray and EUV spectrometer, the measured $E1$ transition wavelengths for ${\mathrm{S}}^{12+}$ and $\mathrm{C}{\mathrm{l}}^{13+}$ were determined to be $256.6852\left(53\right)\AA$ and $237.8037\left(62\right)\AA$ (in vacuum), achieving relative uncertainties of 21 ppm and 26 ppm, respectively. Furthermore, the $E1$ transition energies for these ions were evaluated with ultra-high precision within an ab initio quantum electrodynamics (QED) framework to enable a stringent comparison with the experimental data. The measured values are in good agreement with the theoretical predictions, providing a precision test of QED and correlation effects in few-electron highly charged ions.

Using time-resolved infrared–vacuum-ultraviolet double-resonance spectroscopy, experimental room-temperature measurements of state-to-state rate coefficients for rotational energy transfer within the $X{}^1{\mathrm{\Sigma }}^{+}(v=2)$ vibrational state of CO due to ${\mathrm{H}}_2$ collisions have been compared to accurate four-dimensional close-coupling quantum calculations. Theoretically predicted quantum interferences in the ${\text{CO-H}}_2$ collisional system are experimentally observed at room temperature, and excellent agreement between theory and experiment is observed. These results provide a valuable benchmark for validating the anisotropic part of the potential energy surface, thereby supporting the theoretical modeling of CO emission in warm astrophysical environments such as photodissociation regions.

In this study, we examine the interaction of low- to intermediate-energy electrons $(0–45\mathrm{eV})$ with carbonyl sulfide. These collisions lead to the formation of several anionic fragments, including ${\mathrm{C}}^{-}, {\mathrm{O}}^{-}, {\mathrm{S}}^{-}$, and ${\mathrm{SO}}^{-}$. When the incident electron energy is below the first ionization potential of the molecule, the dissociative electron attachment (DEA) process dominates, primarily yielding ${\mathrm{O}}^{-}$ and ${\mathrm{S}}^{-}$ fragments. At higher energies, beyond the ionization potential, ion-pair dissociation becomes the dominant process, resulting in the emergence of additional fragments such as ${\mathrm{C}}^{-}$ and ${\mathrm{SO}}^{-}$. This leads to an increasingly intricate mechanism, necessitating a detailed analysis to elucidate the ion-pair dissociation pathways. The absolute cross section for ${\mathrm{S}}^{-}$ ions has been determined using the well-established relative flow technique. Theoretical cross sections are calculated using the multiconfigurational time-dependent Hartree method, with each potential energy curve obtained from equation-of-motion coupled-cluster singles and doubles calculations. The computed values are in excellent agreement with the experimental data. The analysis reveals that both linear and bent anionic resonant states contribute to the dissociation process. As the electron energy increases, nuclear rearrangement becomes an indispensable component of the fragmentation dynamics. Due to low count rate, only relative cross section curves have been obtained for the ${\mathrm{O}}^{-}$ and ${\mathrm{SO}}^{-}$ ions. At higher energies, the ion-pair thresholds are evaluated using the Wannier threshold law, yielding values consistent with those derived from thermochemical data.

We present a theoretical investigation of the level population evolution and charge-state kinetics of Kr atoms driven by ultrafast soft x rays in the 210–300-eV range, using a time-dependent rate-equation framework, which is based on a fine-structure-level approach combined with large-scale Monte Carlo simulations. Photoexcitation, photoionization, radiative decay, and single- and direct-double-Auger-decay (DDAD) channels are considered in the present calculation. The effects of DDAD on level population evolution and charge-state distribution are demonstrated quantitatively. This higher-order process, often neglected in previous studies, is shown to contribute approximately 10% to the yields of ${\mathrm{Kr}}^{2+}$ and ${\mathrm{Kr}}^{3+}$. Our results demonstrate that omitting DDAD can lead to systematic underestimation of low charge-state populations, thereby impacting the interpretation of x-ray free-electron-laser (XFEL) experiments. The present work establishes the necessity of including multielectron-decay pathways in precision modeling of inner-shell kinetics in heavy atoms interacting with XFEL.

We show that two-component Bose-Einstein condensed mixtures, in presence of a persistent current, exhibit a nontrivial Doppler shift of the sound velocities. The peculiarity is due to the interspecies interaction and the possibility of generating a counterflow persistent current. Analytical predictions are derived using superfluid hydrodynamics. While the existence of anomalous Doppler shifts at finite temperature has been discussed a long time ago in the case of superfluid ${}^4\mathrm{He}$, an experimental verification of the effect is still missing. For this reason, we also propose a protocol for the measurement of the Doppler shifts, based on the density-density response function. The dynamical protocol is simulated by means of coupled Gross-Pitaevskii equations.

We study a one-dimensional system of interacting anyons with short-range interactions under external confinement. This model, which describes anyons with zero-range $s$-wave and $p$-wave scattering interactions in the strong interaction regime, continuously interpolates between spin-polarized fermions with $p$-wave interactions and free bosons. At zero temperature, the correlation functions decay exponentially with distance, with oscillations governed by the statistics parameter. The decay rate is maximal for $p$-wave fermions and decreases monotonically as the statistics parameter approaches the bosonic limit, where it vanishes. The momentum distribution is asymmetric, a hallmark of one-dimensional anyons, and takes the form of a shifted Lorentzian with universal power-law tails, ${lim}_{k\to \pm \infty }n\left(k\right)\sim C/k^2$. We prove analytically that, following release from a harmonic trap, the asymptotic momentum distribution converges to that of free bosons in the same trap, a phenomenon known as dynamical bosonization. We also establish the universality of the ground-state $n$-particle reduced density matrices: their natural occupations are independent of the confining potential, while the associated natural $n$-point functions for different confinements are related through a simple analytical transformation. In particular, for the one-particle reduced density matrix, we derive exact expressions for both the natural occupations and the natural orbitals at arbitrary particle number. These results extend and unify earlier partial findings for $p$-wave fermions, and they provide a clear conceptual explanation of the double degeneracy observed in their spectrum.

An impurity immersed in a Bose condensate can form a quasiparticle known as a Bose polaron. When the impurity-boson interaction is short ranged and three-body Efimov correlations are neglected, the quasiparticle properties can be characterized in terms of the impurity-boson scattering length $a_{\mathrm{IB}}$ and the condensate coherence length $\xi$. This description remains valid irrespective of the bath density $n_0$. Long-ranged interactions—such as provided by Rydberg or ionic impurities—introduce an effective interaction range $r_{\mathrm{eff}}$ as the third length scale. The interplay among these competing length scales raises the question of whether a robust description across different bath densities can still be maintained. In this study, we discuss the quasiparticle nature of long-range impurities and its dependence on the length scales $n_0^{-1/3}, r_{\mathrm{eff}}$, and $\xi$. We employ two complementary theories—the coherent-state ansatz and the perturbative Gross-Pitaevskii theory—which incorporate beyond-Fröhlich interactions. We derive an analytical expression for the beyond-Fröhlich effective mass for a contact interaction and numerically compute the effective mass for long-range impurities. We argue that the coupling parameter $|a_{\mathrm{IB}}|n_0^{1/3}$ remains the principal parameter governing the properties of the polaron. For weak ($|a_{\mathrm{IB}}|n_0^{1/3}\ll 1$) and intermediate ($|a_{\mathrm{IB}}|n_0^{1/3}\simeq 1$) values of the coupling parameter, long-range impurities in a Bose condensate are well described as quasiparticles with a finite quasiparticle weight and a well-defined effective mass. However, the quasiparticle weight becomes significantly suppressed as the effective impurity volume is occupied by an increasing number of bath particles ($r_{\mathrm{eff}}{n}_0^{1/3}\gg 1$).

Optical whispering-gallery-mode (WGM) microcavities have gained tremendous attention as key elements in photonic applications. Among the coupling techniques for introducing light into the microcavity to pump WGM resonances, free-space coupling presents a straightforward and convenient way for transferring light into microcavities, which eliminates the requirement for additional assistant coupling components. Nevertheless, achieving simplified designs without compromising robustness and high efficiency in free-space coupling systems remains a significant challenge. Here, we demonstrate free-space coupling in ultrathin spiral microtube cavities, achieving a remarkable enhancement in coupling efficiency of up to 32.02%. This significant improvement is enabled by the combination of the ultrathin cavity wall (i.e., the nanomembrane frame of the tube) and a nanonotch. In particular, our design exhibits angle dependence, which provides phase-difference-steered flexible excitation of mode profiles, ranging from peaks, Fano-type curves, to dips. Our straightforward strategy of free-space coupling avoids the complex designs of luminescent materials, precise alignments, and mechanical instability of coupling components, greatly facilitating fundamental explorations on light–matter interactions and related applications.

We demonstrate numerically that upon scanning the pump frequency, controllable switching of the platicon propagation direction (rotation switching) can be observed in normal-dispersion photonic-crystal microresonators. During the forward scan, platicon generation first occurs in the backward wave; as the pump frequency detuning increases, this state may transform into the forward-wave platicon regime. The parameter range for this phenomenon is determined: larger pump amplitudes require larger pump mode-splitting values. With a further increase in the pump amplitude, switching from the backward-wave breather to the forward-wave platicon takes place. The discussed switching effect is reversible: during the backward pump frequency scan, the forward-wave platicon transforms into a platicon or platicon breather in the backward wave. At sufficiently high pump amplitudes, the outcome of this process becomes probabilistic, depending on the particular realization of the input conditions.

Classical nonlinear optical waves propagating in multimode fibers typically exhibit complex interference patterns due to mode interactions. Under high optical power input, however, a distinctive phenomenon known as beam self-cleaning (BSC) emerges, characterized by the spontaneous redistribution of the optical power into the fiber's fundamental mode, resulting in a stable, Gaussian-like beam profile at the output. This study analyzes modal dynamics in graded-index multimode fibers, highlighting the robustness of BSC against perturbations such as fiber bending. Our results reveal that quasiresonance conditions among propagation constants effectively sustain BSC, even when strict four-wave mixing resonance conditions are disrupted. The analysis further suggests employing fibers with a larger refractive index difference as a practical strategy to enhance BSC robustness. Additionally, simulations incorporating Gaussian random variables in propagation constants confirm that the perturbations described by the corrections have a limited impact on the equilibrium mode occupancy distribution. These findings shed light on the mechanisms underpinning the persistence of BSC under realistic perturbations, providing guidelines for optimizing multimode fiber performance in high-power lasers and optical communication systems.

The evolution of quantum states of light in free-space channels is strongly influenced by atmospheric turbulence, posing a significant challenge for quantum communication. The transmittance in such channels randomly fluctuates. This effect is commonly described by the probability distribution of transmittance (PDT). The elliptic-beam approximation provides an analytical model for the PDT, showing good agreement with experimental and simulation data within a specific range of channel parameters. In this work we introduce the circular-beam approximation—a simplified alternative that offers satisfactory accuracy while significantly reducing computational complexity. Our method naturally leads to a technique for determining the model parameters from the first two moments of the transmittance. This approach eliminates the model misspecification bias inherent in the elliptic-beam approximation and significantly extends the applicability range of the PDT model, providing a practical tool for characterizing atmospheric channels in quantum applications.

The $\mathrm{He}+\mathrm{He}+{\mathrm{Na}}^{+}\to \mathrm{He}+\mathrm{He}{\mathrm{Na}}^{+}$ and $\mathrm{He}+\mathrm{He}+{\mathrm{K}}^{+}\to \mathrm{He}+\mathrm{He}{\mathrm{K}}^{+}$ termolecular association reactions are studied at low temperature using both the Monte Carlo classical trajectories and quantum close-coupling approaches. In order to achieve this objective, two potential energy surfaces are constructed, and the bound and quasibound states of the resulting diatomic cations are calculated. The quantum approach is developed within the two-step mechanism. The first step involves the formation of a metastable diatomic system in thermal equilibrium with a system of two freely moving atoms. The second step is the relaxation step, where the collision of the metastable diatomic system with a third atom may produce a stable diatomic system. The relaxation rates are calculated by an accurate quantum collision approach, and the three-body association rates is obtained within the framework of the local thermodynamic equilibrium hypothesis. The comparison between the classical and quantum approaches allows us to gain complementary insight into the temperature dependence of the three-body association rate.

We report experimental investigations of the two-body Coulomb explosion of ammonia molecules, i.e., ${\mathrm{NH}}_3{}^{2+}\to {\mathrm{NH}}_2{}^{+}+{\mathrm{H}}^{+}$, in a phase-controlled linearly polarized laser field. By inspecting the measured kinetic energy release of the fragments, we identify three fragmentation pathways that involve different dication states. The emission direction of ${\mathrm{NH}}_2{}^{+}$ fragments in those three pathways exhibits different two-color phase dependence, unraveling distinct asymmetric dissociation of ${\mathrm{NH}}_3{}^{2+}$. We show that the asymmetric dissociation of ${\mathrm{NH}}_3{}^{2+}$ can be explained by the asymmetric profile of relevant molecular orbitals along the dissociated N-H bond direction.